circle
set of points in a plane at a certain distance from a given point in the plane
center
the given point that the other points in the plane surround
radius
1/2 diameter, the distance for the set of points to the center
chord
line segment whose endpoints are any two points on a circle
secant
a line intersecting a circle that contains a chord
diameter
chord that contains the center of the circle
tangent
a line in the plane of a circle that intersects the circle in exactly one point
point of tangency
the point where a tangent intersects a circle
congruent circles are circles that have
congruent radii
concentric circles
circles that lie in the same plane and have the same center
concentric spheres
spheres that have the same center
inscribed polygon
A polygon whose vertices all lie on a circle.
circumscribed circle
Every vertex of the polygon lies on the circle.
if a line is tangent to a circle
then the line is perpendicular to the radius at point of tangency
if a line in the plane of a circle is perpendicular to a radius at its outer endpoint
then the line is tangent to the circle
tangents to a circle from a point
are congruent
common internal tangent
intersects the segment that joins the centers of the two circles
common external tangent
does not intersect the segment that joins the centers of the two circles (like across the tops of the circles)
tangent circles
coplanar circles that are tangent to the same line at the same point
internally tangent circles
two circles that are tangent and one circle inside the other circle
externally tangent circles
two circles that are tangent and do not share any interior space
circumscribed polygon
polygon that surrounds a circle with each of its sides tangent to the circle
inscribed circle
A circle in which each side of the polygon is tangent to the circle.
central angle
an angle whose vertex is the center of the circle
arc
a continuous portion of a circle
minor arc
part of a circle that measures less than 180 (less than a semi-circle)
major arc
part of a circle that measures from 180 to 360 (equal to or bigger than a semi-circle)
semicircle
an arc of a circle whose endpoints are the endpoints of a diameter (measures 180)
measure of a minor arc
the measure of its central angle
measure of a major arc
the difference between 360 and its minor arc.
arc addition postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs
congruent arcs
arcs that have the same measure and are in the same circle or in congruent circles
in the same circle or in congruent circles, two minor arcs are congruent
if and only if their central angles are congruent(not congruent circles = not congruent arcs)
arc of a chord
the minor arc that a chord cuts off
in the same circles or in congruent circles (arcs + chords)
1. congruent chords have congruent arcs2. congruent arcs have congruent chords
a diameter that is perpendicular to a chord
bisects the chord and its arc
congruent chords and distance in congruent circles or in the same circle
1. congruent chords are equidistant from the center2. 2 chords equidistant from the center are congruent
inscribed angle
an angle whose vertex is on a circle and whose sides contain chords of the circle
measure of an inscribed angle
1/2 the measure of the intercepted arc
if two inscribed angles intercept the same arc
then they are congruent
an angle inscribed in a semi-circle
is a right angle
if a quadrilateral is inscribed in a circle
then opposite angles are supplementary
measure of an angle formed by a chord and a tangent
1/2 the measure of the intercepted arc
measure of an angle formed by 2 chords that intersect inside a circle
half the sum of the intercepted arcs
measure of an angle formed by 2 secants
1/2 the difference of the intercepted arcs
measure of an angle formed by 2 tangents
1/2 the difference of the intercepted arcs
measure of an angle formed by a secant and a tangent
1/2 the difference of the intercepted arcs
if the vertex of an angle is at the center of a circle
angle = measure of intercepted arc
if the vertex is on the circle
angle = 1/2 measure of intercepted arc
if the vertex is inside of a circle but not on the circle or at the center
angle = 1/2 sum of intercepted arcs
if the vertex is outside the circle
angle = 1/2 difference of intercepted arcs
when two chords intersect inside a circle
the product of the segments of one chord = product of the segments of the other chord
secant segment
A segment containing a chord of a circle with one endpoint on the circle
external segment
the part of the secant segment that is outside the circle
when 2 secant segments are drawn to a circle from an external point
the product of one secant segment and its external segment = the product of the other secant segment and its external segment
tangent segment
A segment of a tangent with one endpoint on the circle.
when a secant segment and a tangent segment are drawn to a circle from an external point
the product of the secant segment and its external segment = the square of the measure of the tangent segment